Talk:MHD reconnection

Contents

Reviewer A

The original article on Reconnection was missing a crucial point, viz.the
rate of reconnection. That needed to go into the article somewhere. So I
wrote a couple of pages (attached) that might be tacked on at the end,
or,better, placed appropriately somewhere within the article. I sent a
copy of my remarks to the author, Eric Priest, who acknowledged receipt
and said that he would introduce an abridged version of my writing. I am
pleased that he will go ahead and work the missing material into his
article. This is all in the spirit of an "old fashioned peer review".
But it lies outside the official electronic channels

Reconnection Rate

An essential feature of any process, such as magnetic reconnection, is the rate. The characteristic diffusion time across a scale l is￼, where ￼ is the resistive diffusion coefficient. For ionized hydrogen Ohmic resistance provides the diffusion ￼ m2 /s for a temperature T. This is a lower limit on the effective diffusion process, of course, because of the possibility of plasma turbulence. In any case, it is apparent that the process of magnetic diffusion proceeds too slowly, even on the smallest observable scales, to compete with the ongoing dynamical effects in space and in the Sun. For instance, the coronal magnetic field is continually manipulated by the photospheric granule motions of 1 km/s on scales of 300 km and times scales of 300 s. These motions may produce scales l = 100 km, providing a characteristic diffusion time of 2.5 ￼s, almost 10 3 yrs. A scale of 10 km reduces the time to 10 yrs. Comparing this with the characteristic dynamical time of 300 s for the granule manipulations suggests that diffusion and reconnection can be neglected. Only among the neutral atoms of the photosphere is there enough resistivity ￼ to reduce the characteristic diffusion time across 100 km to an hour or less, and even that provides only a modest reconnection effect.

It is evident, then, that magnetic reconnection is of interest primarily in those situations where the magnetic stresses concentrate the magnetic field gradient into a very thin layer, providing much faster diffusion and reconnection. The original Sweet-Parker reconnection scenario involved pressing together the bipolar fields of two sunspot pairs. The essential feature of this configuration was that the two opposite fields pressed against each other, squeezing the plasma out from between so that the field gradient increased without bound as the two fields approached each other. The characteristic scale l decreased without limit until the diffusion speed ￼became as large as the inflow speed. The inflow speed is determined by how fast the plasma can be expelled along the field lines to regions of lower pressure by the magnetic pressure ￼. The resulting Alfven speed then controls the inflow through the conservation equation (9), and a steady state arises when ￼ becomes equal to the inflow speed. The reconnection velocity, given by the inflow velocity across the broad scale L of the magnetic field, has an Alfvenic Mach number of￼. Were it not for the magnetic stresses compressing the current sheet to such small thickness, the equivalent rate would be much smaller, ￼, where ￼ is 106 – 1012 , it will be recalled.

Then the Petschek reconnection mode, where the Sweet-Parker reconnection is confined to a very small region near the neutral point, provides even faster reconnection, with an inflow Alfvenic Mach number of as much as 0.01 – 0.1. The conclusion is that the reconnection rate varies enormously, depending on the local circumstances. The laboratory experiments of Yamada and coworkers show the basic Sweet-Parker mode, which can go over into the Petschek mode if the effective resistivity at the neutral point is suitably enhanced. Biskamp had earlier described this behavior on the basis of his numerical simulations. The theoretical work of Drake and coworkers goes a step farther to show that the magnetic stresses may squeeze the thickness l of the current sheet to such small values as to approach the ion cyclotron radius and the ion inertial length, so that MHD cannot handle the dissipation properly. The calculation must include plasma kinetics, with the ions decoupling form the magnetic field in the current sheet. Proper treatment of the plasma kinetics shows greatly enhanced dissipation and reconnection rate, and is more favorable for the Petschek mode. That is to say, it supplies the enhanced dissipation around the neutral point necessary for the Petschek mode to arise. These developments leave little doubt that rapid reconnection plays a role in most active dynamical situations.

The theory of dynamically driven reconnection in the diverse geometries of 3D magnetic fields is more complicated, as already noted, and is in a state of active exploration. However, it should be recognized that reconnection in 3D is based on the aforementioned principles. Note first that adding a uniform magnetic field perpendicular to a 2D field does nothing to alter the 2D dynamical picture except to add uniform pressure to the system. The result that the Alfvenic Mach number of the inflow of field and plasma is given by ￼ remains unchanged. Note, then, that all continuous 3D magnetic fields can be reduced locally to 2D plus a perpendicular magnetic field component. The only exception would be at a 3D null point, which requires special consideration. So pick a point P anywhere except at a 3D null point, and consider the plane through P that is perpendicular to B at P. Project the local field onto the plane. Obviously the point P is a neutral point in the projected field. It is an O-type neutral point in some regions and an X-type neutral point in other regions. Where the magnetic stresses are not in equilibrium, they may flatten an X-type neutral point somewhere into a current sheet, initiating Sweet-Parker reconnection. That smoldering reconnection may develop into an explosive Petschek reconnection, or it may not, depending upon local plasma conditions and upon the particular geometry and strength of the 3D magnetic field in which it arises.

Reviewer A:

For the benefit of the reader who is not familiar with magnetic reconnection, I suggest that the sentences around line 10 be expanded to state explicitly what is meant by an ideal medium and what is required to cause reconnection. Paraphrasing the existing sentences, I suggest modifying the statement in the following way:

On large scales the plasma behaves like an ideal medium, with little or no resistive dissipation of any form, and hence no significant magnetic diffusion and reconnection. So the plasma elements preserve their magnetic connections. On the other hand, magnetic reconnection exists where the magnetic stresses create a thin localized region of small thickness L (<<Le) say, wherein the steepened field gradients create intense electric currents and non-ideal effects, e.g. resistive dissipation, Hall effect, etc. become important. The magnetic connectivity of the plasma elements is not preserved in the ensuing field line reconnection.

Reviewer B:

The article is well written and give a nice overview of 2D and 3D reconnection. Some parts, however, might be difficult to understand for a non-expert reader. I, therefore, have some remarks/suggestions for improvement or clarification:

1) MHD is a macroscopic theory while magnetic reconnection occurs on length scale << L_e. Hence, the title 'MHD reconnection' is intriguing and I advise the author to elaborate on this and explain how and what MHD can mean for magnetic reconnection although this model is meant for long length scale phenomena.

5) In Subsection '2D null points it should be mentioned in the second sentence what equation is being linearized.

6) I miss a discussion on the effect of the tearing instability. After the Subsection on Petschek's model, I would add something like:

"In resistive linear tearing instability studies a wavelike perturbation is applied to the whole plasma in a static configuration, which results in wavelike breakup of magnetic topology in the center of the system (Furth, Killeen, Rosenbluth, 1963). Applied to a magnetic reconnection current sheet, the sheet would be practically always unstable, leading to faster reconnection. The outflow from a current sheet of finite width is found to have a stabilizing effect on the tearing instability (Bulanov, Sakai, Syrovatskii, 1979). This accounts for the observed prolonged existence of the current sheets. Once a numerical current sheet has been formed with a finite width it might go unstable to the tearing mode instability on a time-scale tau ~ sqrt(tau_d tau_A). Numerical experimentation has shown that the tearing mode can evolve nonlinearly into a regime of fast reconnection. When the diffusion region becomes too long it goes unstable to tearing and coalescence - impulsive bursty regime (Priest, 1986), characterized by a more rapid energy release in a series of bursts as the islands coalesce. This regime can develop from the Petschek mode going unstable, Sweet-Parker mode going unstable, or from the equilibrium current sheet going unstable to tearing.
Steady-state regimes going unstable to secondary tearing and coalescence were systemized and the criteria leading to the onset of impulsive bursty reconnection criteria are set (Forbes & Priest, 1987)."